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Conditional Probability

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There isn’t enough information. The problem is intractable.
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If we assume that there is no connection between the age and gender, then we don't get any new information from knowing that the person is a man. So the question becomes "what is the probability that a person is between 60-69 years old" which is 42/290.

To see this, note that the probability that a random man is 60-69 years old, is the same as the probability that a random person is 60-69 years old, conditioned on that person being a man.


By the definition of conditional probability, we have

    P(60-69|Man) = P(60-69 and Man)/P(Man)

Assuming that the age and gender of a person are independent, we get


    P(60-69|Man) = P(60-69)*P(Man)/P(Man)
                 = P(60-69)
                 = 42/290 ~ 14.48%.
by
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Not enough information. The separate age distributions for men and women cannot be assumed to be identical.

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